I have a PSD which was delivered to me in CMYK. I need it in RGB for web/screen use. How do I convert the color space correctly? if I change the color mode to RGB the black levels are still off.
In CMYK "100% key-color" is not completely black in most applications. This is because when printed it will not be "as dark as it gets". You can make a "darker" black by mixing in cyan, magenta and yellow colors. So this is probably intended by Photoshop.
I guess that you probably would want (more or less) completely black if you are using it for anything on screen.
Have you tried to change the "Intent" and "Use Black Point Compensation" options in the "Convert to Profile" dialog?
This should change the appearance of the black color, though it might have an unwanted effect on the rest of the elements / colors. But you seem like one that would notice if not as desired.
I don't see any problem here. Of-course a little bit of difference will be created since CMYK supports more color range than RGB. Just copy the CMYK values and paste them in the RGB mode as it is. or just copy the color code ( Hex-values ) from the CMYK document and use it in the RBG document.